This traditional pedagogy results in students developing a negative attitude towards mathematics. Many develop a mathematical phobia and believe that they are not a "maths person". When confronted by challenging mathematics they retreat and have no or only poor strategies with which to approach new ideas. This all leads to a decline in the number of students pursuing mathematical learning beyond the years where it is compulsory.
Fortunately there is a growing body of research that shows there is a better way.

We rely on an assessment measure without taking a close look at what it is measuring and we obfuscate the information we need to evaluate the utility of these measures by reducing the results to numerical values.

Identifying what our children need to learn is one of the most important processes within education. For the teacher this is the question they engage with as they design their teaching and learning units. By no means is this an easy task and the teacher must balance multiple factors to ensure that the programmes they design provide their students with the learning they require. Even the most effective sequence of lessons is of little value if what it sets out to teach has little importance in the lives our learners are likely to lead.

We ask lots of questions as we plan for our student's learning. Some of the questions we ask are about where they are with their learning. But perhaps we miss one important question along the way. Maybe we should be asking questions about how our students will apply what they learn?

What makes a team truly great? What are the qualities which allow some teams to perform at a high level while others seem trapped? One approach to this question is to consider a team as though they were a meal. Thinking metaphorically, we ask what are the ingredients that make a great team and how might we combine them to produce the best results?

There are some ideas which seem to translate nicely into fields of thought far from their point of origin. These are ideas which shine a metaphorical light on concepts and allow us to develop a deeper understanding of that concept once we see it from a fresh perspective. Schrödinger's Cat is one such idea.

We are driven by curiosity. It is an innately human quality that has driven us to explore, ask questions, investigate, wonder why and search for a deeper understanding. In a very fundamental way curiosity is the driver of all self-directed learning. It is our desire to find out more, unlock new knowledge and answer our questions (big ones and little ones) that compels us to learn.
Sir Ken Robinson famously and provocatively asked "Do Schools Kill Creativity?". The same question might be asked about curiosity.

Education exists in an uneasy domain and the teaching professional is forced to navigate between a multitude of conflicting tensions. Our education systems are dominated by abundance of voices all shouting for attention and offering a solution to the problems they have diagnosed. Each individual claims expertise and insights gained from years as a student is sufficient experience to allow one to speak with authority. - Educators need to find their voice.

This unavoidable and irreducible complexity means that schools are challenging place to study, to understand and to manage change within. Even for the teacher who spends everyday inside the school there is so much going on that unguided observations and the plans based upon them come with no guarantee of success. - We need a lens and a lever to manage this complexity. - Such a lens is offered by the 'cultural forces'.

How we see ourselves, how we describe ourselves reveals a great deal about how we see 'others'. In May of this year, speaking to the audience of the International Conference on Thinking, Bruno Della Chiesa invited us to consider how we might approach the question of "who we are?". In responding to such a question, what list of affiliations do we invoke to define ourselves?

With the year rushing to a close, this seems like the right time to set goals for the year ahead. To pause and consider what next and make some personal promises.
The trouble is that the history of setting New Year Resolutions is littered with failures. It is so easy at this point in time to make commitments for change and then just a few weeks later to have forgotten what they were.

With the Christmas Holiday's finally here this is the perfect opportunity to catch up on some of that reading which has been delayed while more pressing matters are dealt with. Here are the top items on my holiday reading list. With a project underway that explores a conceptual based approach to teaching mathematics there is a bias in that direction.

Traditional methods of teaching maths have more in common with how we programme a computer that what we might do if we wanted to engage our students in mathematical thinking. We shouldn't be overly surprised then when our students consider mathematics to be all about learning a set of rules that they need to apply in the right order so as to output the correct response. But is there a better way?

Blueback is a beautiful metaphor for life and particularly of the life we live in schools. When looked at close up, with an eye on the details, the experience of school is one of passing and recurring cycles. When looked at from a distance, with an eye on the whole, there are elements of constancy, the throughlines which bring meaning to our experience and which have as their consequence the residuals of education.

Think of a time when you were completely immersed in a learning challenge. A time when you became aware of the need to master a new skill or concept. A situation that took you outside of your comfort zone, when there were times that you became frustrated, when you thought of quitting, downed tools and walked away, but came back time and time again. Maybe it was a problem you had to solve. Maybe it was a challenge you wanted to overcome.

Data occupies a somewhat curious place within education. Mention it to teachers and you tend to get one of two responses. One group will roll their eyes and with great sarcasm how data is "so exciting". The other group responds with something akin to "actually I quite like data" indicating that experience has shown them that they are members of a small group. The question is why do some people find data to be a useful and fascinating tool while others see it as a good method for inducing sleep?

In the contemporary classroom, there is much greater consideration of what the learner does in partnership with their teacher so that they develop the capacity to learn. Classroom routines and structures are designed to engage the learner in a rich process of dialogical learning.

Two forces seem to present the most significant obstacle to educators hoping to achieve these illustrious goals for and with their learners. The first is time, the second is "the system". Together these two factors act as a bulwark to change; the constraints within which progress is able to occur but only to the point that it strikes against the seemingly immutable obstacles.

We send our students many messages about learning, growth, ability, potential. . . Sometimes we are sending these messages deliberately, such as when we talk about growth mindset and the rewards of effort, persistence and risk taking. At other times the messages we send are accidental, incidental and unplanned; these are often the strongest messages we send.